The tendency of the figures in column 5 of the table is to decrease as the catchment area increases. This tendency has long been known, and attempts have been made to found on it formulæ for calculating flood discharges. One such formula is Q = _c_ M^{3/4} where Q is the flood discharge in cubic feet per second and M is the area of the catchment in square miles. The formula is roughly correct, _c_ being a constant for catchment areas of not dissimilar characters and with rainfalls not differing much. But for other cases there is no knowing how _c_ may vary, and this renders the formula practically useless. The author of another such formula quotes cases Nos. 5 and 8 in the above table, and the two cases mentioned at the end of _Art. 2_ as agreeing fairly well with the result of his formula. The tendency just mentioned is due to the fact that every river is composed of tributaries which have their own small catchment areas but are, when measured to the general outlet or point where the discharge is under consideration, of very different lengths, to the improbability of heavy rainfall occurring over all these small areas at such times as to cause the different flood waves to arrive simultaneously at the outlet, and to the facts that in the case of the longer tributaries the flood waves flatten out (_Hydraulics_, CHAP. IX., _Arts. 3_ and _4_) so as to arrive more gradually, and that, unless rain is also falling all along their courses, these longer tributaries undergo losses from evaporation and absorption. But occasionally it happens that the various flood waves do arrive at the outlet more or less simultaneously, and that the rainfall continues so long and is so widely distributed--though not necessarily of the same intensity as that which caused the flood--that the flood waves do not flatten out and that losses in the channels do not occur. Floods can thus vary to an extraordinary degree in severity, and formulæ are quite useless. This is why floods occur surpassing all previous records, as, for instance, the recent floods in Paris. However severe a flood may be, it can never be said that the maximum has, even probably, been attained unless it can be shown that the rainfall has been so heavy, so long continued, and so distributed that anything worse is not likely to occur.